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MR2063106 (2005g:11080) 11F70
Anandavardhanan, U. K. (6-TIFR-SM); Kable, Anthony C. (1-OKS);
Tandon, R. (6-HYDR-DMS)
Distinguished representations and poles of twisted tensor L-functions. (English summary)
Proc. Amer. Math. Soc. 132 (2004), no. 10, 28752883 (electronic).
Let E/F be a quadratic extension of non-Archimedean local fields of characteristic zero. Suppose
is an admissible representation of G = GLn(E) that is parabolically induced from discrete series
representations. If HomH(, 1) = 0, with H = GLn(F), then let us say that is distinguished.
An important conjecture of Flicker and Rallis correlates the distinguished representations of G
with the representations of G which are base change lifts from a unitary group in n-variables.
Furthermore, Flicker's theory of the twisted tensor L-function (also known as the the Asai L-
function) ties distinguishedness to the existence of a pole for the twisted tensor L-function at 0. A
related conjecture of Jacquet gives a relation between distinguishedness and a symmetry condition
on with respect to the nontrivial element of Gal(E/F).
In this paper, it is shown that HomM (, 1) has dimension one, where M is the mirabolic
subgroup of H, and a specific spanning element l is constructed (using a Whittaker model for